diff --git a/rsa.py b/rsa.py index 1c4e32b..eeee00c 100755 --- a/rsa.py +++ b/rsa.py @@ -5,14 +5,48 @@ import math import os +import decimal def main(): - #Prime of size 32 bit random - print(getPrime(32)) + #Primes of size 32 bit random + #resulting in a 64-bit key mod + p = getPrime(32) + print("p: ", p) + q = getPrime(32) + print("q: ", q) + n = p*q + print("n: ", n) + print("%d bit key" % n.bit_length()) + + #lamda(n) = LCM(p-1, q-1) + #Since LCM(a,b) = ab/GCD(a,b) + #gcd = math.gcd(p-1, q-1) + #print("GCD: ", gcd) + #lcm = abs((p-1) * (q-1)) / gcd + #print("LCM: ", lcm) + phi = (p-1)*(q-1) + print("phi: ", phi) + #e exponant should be 1 < e < lamda(n) and GCD(e, lamda(n)) = 1 (coprime) + # recommended value is 65,537 + e = 65537 + d = pow(e,-1,phi) + print("d: ", d) + print("--------------") + print("public key (%d, %d)" % (n,e) ) + + msg_text = "Hello" + msg_number_form = int.from_bytes(msg_text.encode(),"little") + print("Message: %s or %d" % (msg_text, msg_number_form)) + + msg_encrypted_number_form = pow(msg_number_form, e, n) + print("Encrypted msg: ", msg_encrypted_number_form) + msg_decrypted_number_form = pow(msg_encrypted_number_form, d, n) + print("Decrypted msg: ", msg_decrypted_number_form) def getPrime(bits): while True: + #Byte order "little" or "big" does not matter here since we want a random number from os.urandom() x = int.from_bytes(os.urandom(int(bits/8)),"little") if isPrime(x): return x